CNN, citing sources close to the Romney family, says it's unlikely, largely because Romney's wife, Ann, is thought to be opposed to a third grueling campaign for president.
But after "Mitt," a campaign documentary was released showing a side of the candidate many Americans never saw -- funny, humble, pious, devoted father and husband -- some are questioning whether the 2012 Republican nominee might be the right choice again in 2016.
The rumblings come after a particularly rough month for fellow Republican, New Jersey Gov. Chris Christie, who's become embroiled in "Bridgegate" -- after it became known close aides allegedly closed lanes on the George Washington Bridge as a form of political retribution against a Democratic mayor who refused to endorse Christie's re-election campaign.
Christie has been frequently mentioned as a potential GOP presidential candidate, as has Rep. Paul Ryan, a Wisconsin congressman, chair of the House Budget Committee and Romney's running mate in 2012.
As for Romney himself, he told CNN in June he would "love" to run for president again but it would have to be a family decision.
"I would do it again, but it's not my time. Ann might not ... but I would love to do it again, are you kidding? I'd love to do it and win. But it's not my time. I've had my chance."
2014: The Year in Music [PHOTOS]